Polygonal Finite Element for Two-Dimensional Lid-Driven Cavity Flow

This paper investigates a polygonal finite element (PFE) to solve a two-dimensional (2D) incompressible steady fluid problem in a cavity square. It is a well-known standard benchmark (i.e., lid-driven cavity flow)-to evaluate the numerical methods in solving fluid problems controlled by the Navier-Stokes (N-S) equation system. The approximation solutions provided in this research are based on our developed equal-order mixed PFE, called Pe(1)Pe(1). It is an exciting development based on constructing the mixed scheme method of two equal-order discretisation spaces for both fluid pressure and velocity fields of flows and our proposed stabilisation technique. In this research, to handle the nonlinear problem of N-S, the Picard iteration scheme is applied. Our proposed method's performance and convergence are validated by several simulations coded by commercial software, i.e., MATLAB. For this research, the benchmark is executed with various Reynolds numbers up to the maximum Re = 1000. All results then numerously compared to available sources in the literature.

Automated summary

This paper investigates a polygonal finite element (PFE) method to solve a two-dimensional incompressible fluid problem. The method is validated using lid-driven cavity flow as a benchmark, and it employs an equal-order mixed finite element method and a stabilisation technique. The nonlinear problem is handled using the Picard iteration scheme, and the method's performance and convergence are verified through simulations using MATLAB. The results are compared with available data from the literature.